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https://arxiv.org/abs/1705.06283

Yasunori Nomura, Pratik Rath, Nico Salzetta

(Submitted on 17 May 2017)

We argue that classical spacetimes represent amplified information in the holographic theory of quantum gravity. In general, classicalization of a quantum system involves amplification of information at the cost of exponentially reducing the number of observables. In quantum gravity, the geometry of spacetime must be the analogously amplified information. Bulk local semiclassical operators probe this information without disturbing it; these correspond to logical operators acting on code subspaces of the holographic theory. From this viewpoint, we study how bulk local operators may be realized in a holographic theory of general spacetimes, which includes AdS/CFT as a special case, and deduce its consequences. In the first half of the paper, we ask what description of the bulk physics is provided by a holographic state dual to a semiclassical spacetime. In particular, we analyze what portion of the bulk can be reconstructed in the holographic theory. The analysis indicates that when a spacetime contains a quasi-static black hole inside a holographic screen, the theory provides a description of physics as viewed from the exterior (though the interior information is not absent). In the second half, we study how and when a semiclassical description emerges in the holographic theory. We find that states representing semiclassical spacetimes are non-generic in the holographic Hilbert space; in particular, microstates for a semiclassical spacetime do not form a Hilbert space. When there are a significant number of independent microstates, semiclassical operators must be given state-dependently. We elucidate this point using the stabilizer formalism and tensor network models. We also argue that semiclassical states, albeit exponentially rare in the Hilbert space, can be dynamically selected under time evolution. Finally, we discuss implications of the present picture for the black hole interior.

https://arxiv.org/abs/1705.06711

Matti Raasakka

(Submitted on 18 May 2017)

We show that local Lorentz covariance arises canonically as the group of transformations between local thermal states in the framework of Local Quantum Physics, given the following three postulates: (i) Local observable algebras are finite-dimensional. (ii) Minimal local observable algebras are isomorphic to M2(C), the observable algebra of a single qubit. (iii) The vacuum restricted to any minimal local observable algebra is thermal. The derivation reveals a new and surprising relation between spacetime structure and local quantum states. In particular, we show how local restrictions of the vacuum can determine the connection between different local inertial reference frames.

**Classical Spacetimes as Amplified Information in Holographic Quantum Theories**Yasunori Nomura, Pratik Rath, Nico Salzetta

(Submitted on 17 May 2017)

We argue that classical spacetimes represent amplified information in the holographic theory of quantum gravity. In general, classicalization of a quantum system involves amplification of information at the cost of exponentially reducing the number of observables. In quantum gravity, the geometry of spacetime must be the analogously amplified information. Bulk local semiclassical operators probe this information without disturbing it; these correspond to logical operators acting on code subspaces of the holographic theory. From this viewpoint, we study how bulk local operators may be realized in a holographic theory of general spacetimes, which includes AdS/CFT as a special case, and deduce its consequences. In the first half of the paper, we ask what description of the bulk physics is provided by a holographic state dual to a semiclassical spacetime. In particular, we analyze what portion of the bulk can be reconstructed in the holographic theory. The analysis indicates that when a spacetime contains a quasi-static black hole inside a holographic screen, the theory provides a description of physics as viewed from the exterior (though the interior information is not absent). In the second half, we study how and when a semiclassical description emerges in the holographic theory. We find that states representing semiclassical spacetimes are non-generic in the holographic Hilbert space; in particular, microstates for a semiclassical spacetime do not form a Hilbert space. When there are a significant number of independent microstates, semiclassical operators must be given state-dependently. We elucidate this point using the stabilizer formalism and tensor network models. We also argue that semiclassical states, albeit exponentially rare in the Hilbert space, can be dynamically selected under time evolution. Finally, we discuss implications of the present picture for the black hole interior.

https://arxiv.org/abs/1705.06711

**Local Lorentz covariance in finite-dimensional Local Quantum Physics**Matti Raasakka

(Submitted on 18 May 2017)

We show that local Lorentz covariance arises canonically as the group of transformations between local thermal states in the framework of Local Quantum Physics, given the following three postulates: (i) Local observable algebras are finite-dimensional. (ii) Minimal local observable algebras are isomorphic to M2(C), the observable algebra of a single qubit. (iii) The vacuum restricted to any minimal local observable algebra is thermal. The derivation reveals a new and surprising relation between spacetime structure and local quantum states. In particular, we show how local restrictions of the vacuum can determine the connection between different local inertial reference frames.

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